Question

In: Statistics and Probability

The table below is taken from the Australian Bureau of Statistics website.

 

The table below is taken from the Australian Bureau of Statistics website. It provides data on mortgage repayment (monthly) by Australian households living in different dwelling structures in the year 2011.

Dwelling Structure

Total occupied private dwellings

Separate house

Semi-detached, row or terrace house, townhouse

Flat, unit or apartment

Mortgage Repayment (monthly)

        

Total

2 709 429

2 324 546

190 411

187 375

$0-$299

114 197

99 624

7 352

6 694

$300-$449

64 357

57 107

3 749

3 220

$450-$599

60 317

53 545

3 375

3 112

$600-$799

113 616

101 194

6 224

5 765

$800-$999

146 303

129 290

8 227

8 289

$1,000-$1,399

380 790

331 572

23 386

24 761

$1,400-$1,799

400 688

341 557

27 855

30 434

$1,800-$2,399

548 587

464 033

40 573

42 946

$2,400-$2,999

303 184

256 405

22 677

23 635

$3,000-$3,999

261 122

219 568

21 697

19 333

$4,000 and over

175 821

146 771

16 659

11 781

Mortgage repayment not stated

140 447

123 880

8 637

7 405

a) Find the probability that a randomly selected households live in separate house dwelling?    1 mark

b) In a total occupied private dwellings, what is the probability that a randomly selected households make a monthly mortgage repayment of $800-$999?                                                          1 mark

c) What is the probability that a randomly selected households make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999?                                                                                        1 mark

d) What is the probability that a randomly selected households make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure?

Solutions

Expert Solution

a) The probability that randomly selected households to live in separate house dwelling:

The total dwellings= 2709429

The total separate house dwellings= 2324546

The probability= 2324546/ 2709429 = 0.857947

b)The probability that randomly selected households to make a monthly mortgage repayment of $800-$999:

The total dwellings= 2709429

The total monthly mortgage payments of $800-999= 146303

The probability = 146303 / 2709429 =0.053998

c) The probability that randomly selected households to make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999:

The total dwellings= 2709429

The total dwellings of $1800-2399 =548587

The total dwellings of $2400-2999 =303184

The total dwellings of $1800-2399 or $2400-2999= 548587+303184= 851771

The probability= 851771 / 2709429 =0.314373

d)The probability that randomly selected households to make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure:

The total dwellings= 2709429

The total monthly mortgage repayment of $300-449 in a flat, unit or apartment dwelling= 3220

The probability= 3220/ 2709429 = 0.001188

orchestra answered 2 years ago
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